LLM Hallucination Detection via Low-rank Multilinear Decomposition

Devansh Sharma; Faizul Rakib Sayem; Shahana Ibrahim

cs.CLOct 26, 2026

LLM Hallucination Detection via Low-rank Multilinear Decomposition

Authors: Devansh Sharma, Faizul Rakib Sayem, Shahana Ibrahim

Organizations: Department of Electrical & Computer Engineering, University of Central Florida

Abstract

Large language models (LLMs) frequently generate fluent yet factually incorrect responses, raising concerns about their reliability. Recent hallucination detectors increasingly exploit internal representations, but extracting informative signals from high-dimensional hidden states remains challenging. Existing approaches often rely on selected activations or pooling-based compression, potentially overlooking discriminative information distributed across Transformer layers, feature modes, and tokens. We propose LOTUS (Low-rank Order-statistic TUcker-based Subspace learning), a multilinear low-rank decomposition framework for hallucination detection that extracts compact representations from LLM hidden states while reducing dependence on labeled data. Our approach first summarizes variable-length token representations using complementary statistical descriptors that capture peak activations, activation distributions, and cross-layer changes. We then leverage low-rank multilinear decomposition to extract compact representations that capture the underlying structure of LLM hidden states, which are subsequently used to train a lightweight hallucination classifier. Experiments across multiple LLMs and question-answering benchmarks demonstrate improved hallucination detection performance over recent state-of-the-art baselines.

Figures & tables

Figure 1: Overview of our proposed framework LOTUS . Hidden states are summarized across tokens using peak activations, activation quantiles, and cross-layer differences, projected with summary-specific Tucker-2 bases learned from unlabeled activations, and concatenated for lightweight hallucination classification.

Qwen2.5-7B-Instruct
Method	NQ-Open	TruthfulQA	TriviaQA	TyDiQA-GP
Perplexity	$57.58$	$65.36$	$75.42$	$55.72$
LN-Entropy	$63.24$	$59.61$	$73.96$	$68.60$
Semantic Entropy	$61.91$	$60.86$	$63.49$	$51.60$
Lexical Similarity	$65.95$	$58.44$	$71.09$	$72.86$
EigenScore	$62.14$	$56.24$	$70.84$	$63.48$

Table 1: Pooled AUROC (%) under the question-level split across two LLMs and four QA benchmarks. Results are averaged over five random trials; mean

\pm

standard deviation is reported for supervised detectors. Best results are in bold.

	Qwen2.5-7B-Instruct		LLaMA-3.1-8B
Method	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
HARP	$67.84\pm 2.07$	$82.69\pm 1.44$	$67.78\pm 8.05$	$75.87\pm 1.63$
ACT-ViT	$78.51\pm 4.51$	$81.93\pm 1.93$	$83.50\pm 3.12$	$80.50\pm 2.34$
LOTUS (Ours)	$\mathbf{82.07\pm 2.18}$	$\mathbf{88.09\pm 3.77}$	$\mathbf{82.73\pm 1.92}$	$\mathbf{81.34\pm 3.01}$

Table 2: Within-question AUROC (%) under the question-level split. Results are reported as mean

\pm

standard deviation over five random trials.

Qwen2.5-7B-Instruct
		AUROC / $\Delta$ vs. LOTUS
Configuration	Summaries	NQ-Open	TruthfulQA	TriviaQA	TyDiQA-GP
LOTUS (full)	$\bm{C},\bm{S},\bm{V}$	$\mathbf{79.29}$	$\mathbf{87.83}$	$\mathbf{91.69}$	$\mathbf{87.86}$
Ablated variants
w/o $\bm{S}$	$\bm{C},\bm{V}$	$+0.15$	$-0.04$	$-0.23$	$-0.06$
Peak only	$\bm{C}$	$-0.48$	$-0.75$	$-0.41$	$+0.40$

Table 3: The full LOTUS configuration independently projects and concatenates the peak activation (

\bm{C}

), activation quantile (

\bm{S}

), and cross-layer difference (

\bm{V}

) summaries. The LOTUS row reports absolute pooled AUROC (%), while all ablated variants report the change in AUROC relative to LOTUS (

\Delta

). Positive values indicate improvement over LOTUS and negative values indicate degradation. Results use the question-level split and are averaged over five random draws.

Qwen2.5-7B-Instruct $\rightarrow$ LLaMA-3.1-8B
	TruthfulQA		TyDiQA-GP
Method	Pooled	Within	Pooled	Within
Target-trained LOTUS	$89.22\pm 1.44$	$82.73$	$82.47\pm 1.24$	$81.34$
Transfer + alignment	$\mathbf{87.44\pm 1.18}$	$\mathbf{80.67}$	$\mathbf{77.26\pm 2.32}$	$\mathbf{78.44}$
Transfer w/o alignment	$63.73\pm 4.93$	$66.10$	$48.79\pm 2.31$	$50.60$
LLaMA-3.1-8B $\rightarrow$ Qwen2.5-7B-Instruct

Table 4: AUROC (%) on the target model under the question-level split. Target-trained uses target labels, while transferred detectors reuse the source classifier with or without unlabeled ridge alignment. Pooled AUROC is mean

\pm

standard deviation over five draws; within-question AUROC is also reported.

Figure 2: Covariance spectra of the peak activation matrix for Qwen2.5-7B-Instruct on TyDiQA-GP, at every layer. (a) effective rank of correct and hallucinated responses, (b) hallucinated-to-correct effective-rank ratio under size-matched and question-paired sampling, and (c) single-layer AUROC. Shaded bands indicate

95\%

intervals; the gray region marks the LOTUS layer window.

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Table 7

Qwen2.5-7B-Instruct
Window (blocks)	TruthfulQA	TyDiQA-GP
$3$ – $11$	$87.17$	$84.93$
$7$ – $15$	$87.13$	$87.04$
$11$ – $19$	$87.52$	$87.27$
$13$ – $21$	$87.92$	$87.48$
$15$ – $23$ (reported)	$87.50$	$87.89$

Appendix

Table 5: Pooled AUROC (%) under the question-level split, averaged over five different runs. Results are reported across different nine-layer windows while keeping all other settings fixed.

	TyDiQA-GP		TruthfulQA
Block	Peak	Range	Peak	Range
Embedding	76.5	77.3	82.3	82.3
0	77.5	78.1	83.9	85.0
1	75.3	79.5	83.7	84.9
2	77.2	78.9	85.4	86.3
3	77.3	80.0	85.8	86.5

Appendix

Table 6: Single-layer AUROC (%) for Qwen2.5-7B-Instruct: the peak or range summary of one layer, projected to

64

features and classified by logistic regression, with question-grouped five-fold cross-validation. Blocks are counted from zero; the rules enclose our window, blocks

15

23

Figure 3: Comparison of question-level and answer-level splitting with ten responses per question. Question-level splitting keeps all responses from a known question in one partition, whereas answer-level splitting can place responses from the same question in both training and test sets, affecting

92.6\%

–

95.7\%

of known questions in our data.

	NQ-Open		TruthfulQA		TriviaQA		TyDiQA-GP
Method	Ans.	$\Delta$	Ans.	$\Delta$	Ans.	$\Delta$	Ans.	$\Delta$
Qwen2.5-7B-Instruct
HARP	81.03	$+13.30$	85.16	$+7.62$	92.50	$+3.75$	91.75	$+11.85$
LOTUS	91.14	$+11.85$	94.03	$+6.20$	94.05	$+2.36$	94.72	$+6.86$
LLaMA-3.1-8B
HARP	86.56	$+6.00$	84.84	$+5.26$	88.08	$+5.54$	85.65	$+10.66$

Appendix

Table 7: Pooled AUROC (%) of HARP and LOTUS under the answer-level split (Ans.), and its gain over the question-level split (

\Delta

= Ans.

-

question-level AUROC in Table 1 ). ACT-ViT under both splits is in Table 17 . Standard deviations are in Table 16 .

				Qwen2.5-7B		LLaMA-3.1-8B
Reduction	Features	Parameters	Multiply-adds	TQA	TyDi	TQA	TyDi
Tucker-2 (LOTUS)	$896$	$1.15$ / $1.31$	$9.9$ / $11.3$	87.76	87.82	89.22	82.47
Tucker-3, 2 bins, $r_{T}{=}1$	$896$	$1.15$ / $1.31$	$19.7$ / $22.6$	87.86	87.96	89.51	82.67
Tucker-3, 8 bins, $r_{T}{=}8$	$7{,}168$	$1.15$ / $1.31$	$79.1$ / $90.3$	86.84	87.28	89.20	80.96
Flat PCA	$896$	$45.6$ / $52.2$	$45.6$ / $52.2$	88.09	87.45	88.42	81.96
Random projection	$896$	none	$45.6$ / $52.2$	82.87	85.38	84.32	77.24

Appendix

Table 8: Performance comparison of reduction methods using the same random-forest classifier under the question-level split, averaged over five runs on TruthfulQA (TQA) and TyDiQA-GP (TyDi). We report pooled AUROC (%), feature dimension, fitted basis parameters, and projection multiply-adds for Qwen2.5-7B-Instruct / LLaMA-3.1-8B.

		Qwen2.5-7B-Instruct		LLaMA-3.1-8B
Reduction	Parameters	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
Tucker-2 (LOTUS)	1.15M / 1.31M	87.76	87.82	89.22	82.47
Best layer	5.28M / 6.03M	88.05	86.54	89.11	83.12
Layer average	5.28M / 6.03M	87.87	86.97	88.28	80.92

Appendix

Table 9: Single-layer reductions to

896

features with the random forest, under the question-level split: pooled AUROC (%), averaged over five draws. Parameters are the entries of the fitted bases, for Qwen2.5-7B-Instruct / LLaMA-3.1-8B.

Order statistics within bins (peak, range, update)
			Qwen2.5-7B-Instruct		LLaMA-3.1-8B
$B$	$r_{T}$	Features	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
$1$	$1$	$896$	$87.49$	$87.88$	$89.34$	$82.46$
$2$	$1$	$896$	$87.86$ ( $+0.37$ )	$87.96$ ( $+0.08$ )	$89.51$ ( $+0.17$ )	$82.67$ ( $+0.21$ )
$2$	$2$	$1{,}792$	$87.30$ ( $-0.19$ )	$87.79$ ( $-0.10$ )	$89.38$ ( $+0.03$ )	$81.81$ ( $-0.65$ )
$4$	$2$	$1{,}792$	$87.50$ ( $+0.01$ )	$88.07$ ( $+0.18$ )	$89.55$ ( $+0.20$ )	$81.82$ ( $-0.65$ )

Appendix

Table 10: Tucker-3 with

B

token bins and token rank

r_{T}

, with the random forest, under the question-level split: pooled AUROC (%), averaged over five draws, and in parentheses the difference from one bin of the same pooling over the same draws. Features are passed to the classifier.

Qwen2.5-7B-Instruct
Setting		$5\%$	$10\%$	$25\%$	$50\%$	$100\%$
TruthfulQA	Tucker-2	$77.10$	$81.32$	$84.89$	$86.12$	$87.76$
	flat PCA	$+0.09^{\dagger}$	$+0.64$	$-1.85$	$-0.71$	$+0.33$
TyDiQA-GP	Tucker-2	$74.05$	$84.00$	$85.01$	$86.31$	$87.82$
	flat PCA	$-0.18^{\dagger}$	$-5.06^{\dagger}$	$-1.33$	$-1.57$	$-0.38$
LLaMA-3.1-8B

Appendix

Table 11: Reducing the number of labeled training questions, with the test sets held fixed and both reductions refit on each run. For each setting the first row is the pooled AUROC (%) of the Tucker-2 core, averaged over five runs, and the second is the difference of flat PCA of the same width from it, in AUROC points; negative values are below the core. The last row averages the four differences. † At these sizes flat PCA cannot supply all

896

features, since each summary yields at most one component per training response.

Configuration	Summaries	Features	NQ-Open	TruthfulQA	TriviaQA	TyDiQA-GP
Qwen2.5-7B-Instruct
LOTUS (full)	$C,S,V$	$896$	$69.24$	$80.16$	$92.48$	$\mathbf{84.09}$
Ablated variants
w/o $S$	$C,V$	$576$	$68.01$	$81.17$	$92.56$	$81.92$
Peak only	$C$	$320$	$\mathbf{71.85}$	$81.80$	$92.44$	$80.99$
Quantile only	$S$	$320$	$70.43$	$82.07$	$\mathbf{92.69}$	$82.82$

Appendix

Table 12: Pooled AUROC (%) for LOTUS and its ablated variants using logistic regression under the question-level split. Results are averaged over five random draws.

		Qwen2.5-7B-Instruct		LLaMA-3.1-8B
Ranks	Width	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
$k=1$ , $r_{F}=64$	192	88.04	87.41	89.07	81.32
$k=2$ , $r_{F}=64$	320	87.88	87.36	89.82	82.75
$k=3$ , $r_{F}=64$	512	87.63	87.78	89.45	82.81
$k=4$ , $r_{F}=64$	704	87.89	88.03	89.33	82.59
$k=5$ , $r_{F}=64$	896	87.76	87.82	89.22	82.47

Appendix

Table 13: Rank sensitivity under the question-level split, averaged over five runs. We vary one rank at a time, and width denotes the number of features per response.

Detector	TruthfulQA	TyDiQA-GP	NQ-Open	TriviaQA
HARP	none: the last layer’s states are recomputed in its own script
ACT-ViT, $N=20$	$8.7$ – $10.0$	$4.7$ – $5.4$	$38.6$ – $44.1$	$106$ – $122$
ACT-ViT, $N=100$	$43.6$ – $49.9$	$23.5$ – $26.9$	$193$ – $220$	$532$ – $608$
LOTUS	$2.3$ – $2.7$	$1.3$ – $1.4$	$10.4$ – $11.8$	$28.6$ – $32.7$

Appendix

Table 14: Stored input (GB) per model and dataset, float16 and uncompressed, as a range over Qwen2.5-7B-Instruct and LLaMA-3.1-8B.

N

denotes ACT-ViT’s number of tokens, where we report

N=20

and the released default is

N=100

Model, dataset	$N$	Pooled, Q	Pooled, A	Within, Q
Qwen2.5-7B-Instruct, TruthfulQA	$20$	$85.40\pm 1.01$	$87.58\pm 0.56$	$78.51\pm 4.51$
Qwen2.5-7B-Instruct, TruthfulQA	$100$	$85.65\pm 1.74$	$88.18\pm 0.59$	$79.26\pm 3.89$
Qwen2.5-7B-Instruct, TyDiQA-GP	$20$	$82.82\pm 1.46$	$86.81\pm 1.69$	$81.93\pm 1.93$
Qwen2.5-7B-Instruct, TyDiQA-GP	$100$	$84.05\pm 1.52$	$89.93\pm 2.12$	$85.32\pm 2.43$
LLaMA-3.1-8B, TruthfulQA	$20$	$89.07\pm 1.30$	$90.68\pm 0.60$	$83.50\pm 3.12$
LLaMA-3.1-8B, TyDiQA-GP	$20$	$79.43\pm 1.41$	$84.72\pm 1.47$	$80.50\pm 2.34$

Appendix

Table 15: ACT-ViT performance across different numbers of tokens

N

. We report pooled AUROC (%) under question-level (Q) and answer-level (A) splits, and within-question AUROC under the question-level split, averaged over five runs with standard deviations.

Qwen2.5-7B-Instruct
Method, split	NQ-Open	TruthfulQA	TriviaQA	TyDiQA-GP
HARP, Q	$67.73\pm 2.24$	$77.54\pm 1.51$	$88.75\pm 0.33$	$79.90\pm 2.87$
HARP, A	$81.03\pm 2.41$	$85.16\pm 1.23$	$92.50\pm 0.24$	$91.75\pm 0.95$
LOTUS, Q	$79.29\pm 5.24$	$87.83\pm 0.89$	$91.69\pm 0.10$	$87.86\pm 1.95$
LOTUS, A	$91.14\pm 1.01$	$94.03\pm 0.44$	$94.05\pm 0.10$	$94.72\pm 0.74$
ACT-ViT, Q	$79.11\pm 5.80$	$85.40\pm 1.01$	$92.77\pm 0.28$	$82.82\pm 1.46$

Appendix

Table 16: HARP, ACT-ViT and LOTUS under the question-level (Q) and answer-level (A) splits: pooled AUROC (%), mean

\pm

standard deviation over five runs.

	Qwen2.5-7B-Instruct		LLaMA-3.1-8B
Method, split	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
HARP, Q	$77.54\pm 1.51$	$79.90\pm 2.87$	$79.58\pm 5.38$	$74.99\pm 0.88$
HARP, A	$85.16\pm 1.23$	$91.75\pm 0.95$	$84.84\pm 1.91$	$85.65\pm 0.78$
ACT-ViT (joint), Q	$83.13\pm 1.18$	$77.70\pm 2.99$	$86.78\pm 1.20$	$77.21\pm 1.84$
ACT-ViT (joint), A	$87.79\pm 0.36$	$83.88\pm 2.29$	$90.14\pm 0.56$	$81.38\pm 2.80$
ACT-ViT, Q	$85.40\pm 1.01$	$82.82\pm 1.46$	$89.07\pm 1.30$	$79.43\pm 1.41$

Appendix

Table 17: HARP, both ACT-ViT variants and LOTUS on TruthfulQA and TyDiQA-GP under the question-level (Q) and answer-level (A) splits, with standard deviations: pooled AUROC (%), mean

\pm

standard deviation over five draws.

	Qwen2.5-7B-Instruct		LLaMA-3.1-8B
Method	TruthfulQA	TyDiQA-GP	TruthfulQA	TyDiQA-GP
LOTUS	$82.07\pm 2.18$	$88.09\pm 3.77$	$82.73\pm 1.92$	$81.34\pm 3.01$
HARP	$67.84\pm 2.07$	$82.69\pm 1.44$	$67.78\pm 8.05$	$75.87\pm 1.63$
ACT-ViT	$78.51\pm 4.51$	$81.93\pm 1.93$	$83.50\pm 3.12$	$80.50\pm 2.34$
Answer pairs per draw	1,820–2,059	940–1,038	1,840–1,942	1,576–1,768
HARP’s draws	1,896–2,137	924–1,086	1,728–1,930	1,524–1,719

Appendix

Table 18: Within-question AUROC (%) of the three detectors that score each answer, under the question-level split: mean

\pm

standard deviation over five draws. LOTUS and ACT-ViT share the same test sets; HARP uses the draws of its own code. ACT-ViT uses

N=20

Qwen2.5-7B-Instruct
Result	NQ-Open	TruthfulQA	TriviaQA	TyDiQA-GP
Published	84.0	88.1	92.8	88.4
Released split, 1 run	83.12	86.27	92.89	91.87
Released split, 5 draws	$81.03\pm 2.41$	$85.16\pm 1.23$	$92.50\pm 0.24$	$91.75\pm 0.95$
Question-level split, 5 draws	$67.73\pm 2.24$	$77.54\pm 1.51$	$88.75\pm 0.33$	$79.90\pm 2.87$
LLaMA-3.1-8B

Appendix

Table 19: HARP with

256

directions: published AUROC (%) on the authors’ generations, and our runs of the released code on our generations and labels. The released split is the answer-level split; five draws are reported as mean

\pm

standard deviation.

		Known questions			Agreement
Dataset	Questions	Ours	HARP	Changed	Answers	Status
NQ-Open	$3{,}610$	$360$	$358$	$4$	$99.94$	$99.89$
TruthfulQA	$817$	$666$	$670$	$6$	$99.57$	$99.27$
TriviaQA	$9{,}960$	$6{,}316$	$6{,}331$	$33$	$99.71$	$99.67$
TyDiQA-GP	$440$	$302$	$301$	$1$	$99.27$	$99.77$
Total	$14{,}827$	$7{,}644$	$7{,}660$	$44$

Appendix

Table 20: Our labels against those of the released judge of HARP, on the answers of Qwen2.5-7B-Instruct. Changed counts questions whose known or unknown status differs between the two sets of labels; the last two columns give the agreement (%) over answers and over the known or unknown status of questions.

Draw	Layer	C	H	C	H	AUROC
		Effective rank		Top-64 variance
Size-matched	Embedding	$47.3$	$136.6$	$0.715$	$0.575$	$76.5$
	Blocks $15$ – $23$	$97.7$	$204.7$	$0.653$	$0.538$	$86.8$
	Block $27$ (last)	$109.7$	$215.1$	$0.626$	$0.520$	$83.3$
Paired	Embedding	$35.0$	$66.5$	$0.780$	$0.684$	$76.5$
	Blocks $15$ – $23$	$59.6$	$93.4$	$0.716$	$0.650$	$86.8$

Appendix

Table 21: Covariance spectra of peak summaries for correct (C) and hallucinated (H) responses from Qwen2.5-7B-Instruct on TyDiQA-GP, averaged over

20

runs. We report size-matched and question-paired comparisons for the embedding, blocks

15

–

23

, and the final block. The last column reports single-layer AUROC (%) using logistic regression with question-grouped five-fold cross-validation (Appendix C ).

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LLM Hallucination Detection

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Large Language Models (LLMs) are powerful and widely adopted, but their practical impact is limited by the well-known hallucination phenomenon. While recent hallucination detection methods have made notable progress, we find most of them overlook the dynamic nature and underlying mechanisms of it. To address this gap, we propose HalluSAE, a phase transition-inspired framework that models hallucination as a critical shift in the model's latent dynamics. By modeling the generation process as a trajectory through a potential energy landscape, HalluSAE identifies critical transition zones and attributes factual errors to specific high-energy sparse features. Our approach consists of three stages: (1) Potential Energy Empowered Phase Zone Localization via sparse autoencoders and a geometric potential energy metric; (2) Hallucination-related Sparse Feature Attribution using contrastive logit attribution; and (3) Probing-based Causal Hallucination Detection through linear probes on disentangled features. Extensive experiments on Gemma-2-9B demonstrate that HalluSAE achieves state-of-the-art hallucination detection performance.

Abstract

LLM Hallucination Detection

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